Geometry Over Nonclosed Fields (Simons Symposia) by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel

By Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel

Based at the Simons Symposia held in 2015, the complaints during this quantity specialise in rational curves on higher-dimensional algebraic forms and functions of the speculation of curves to mathematics difficulties. there was major growth during this box with significant new effects, that have given new impetus to the research of rational curves and areas of rational curves on K3 surfaces and their higher-dimensional generalizations. One major contemporary perception the booklet covers is the idea that the geometry of rational curves is tightly coupled to houses of derived different types of sheaves on K3 surfaces. The implementation of this concept resulted in proofs of long-standing conjectures relating birational houses of holomorphic symplectic forms, which in flip may still yield new theorems in mathematics. This court cases quantity covers those new insights in detail. 

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